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Sagot :
The curve that passes through the point (1,1) with a given slope is a line.
1. The equation of a line can be determined using the point-slope form of the equation, which is y - y1 = m(x - x1).
2. For the given point (1,1) and slope, the equation of the line is y - 1 = m(x - 1).
3. Substituting the given slope m for the equation, we get y - 1 = m(x - 1).
4. Simplifying the equation, we get y = mx - m + 1.
5. The equation of the line can also be written in the general form of the equation of a line, which is y = mx + b.
6. Substituting the given slope m and the y-intercept b = -m + 1, the equation of the line can be written as y = mx - m + 1.
7. The slope of the line can be determined by calculating the rise (change in y-coordinate) over the run (change in x-coordinate).
8. For the given point (1,1) and another point (x2, y2), the slope can be calculated using the formula m = (y2 - y1)/(x2 - x1).
9. For example, if the second point has coordinates (3, 4), the slope of the line can be calculated as m = (4 - 1)/(3 - 1) = 3/2.
10. The equation of the line can then be determined using the point-slope form of the equation, which is y - y1 = m(x
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